In a team game I played my opponents received a diplo card one full turn before my team did. It was in the first 3 turns and there were no cards supposed to be earned by either team. When I asked them how they did it they said they cheated. I just do not know how.Anyone?????

"If the minimum number of pieces is less than the number of pieces awarded each turn, players will get the minimum and the remainder will be randomed as normal."

This means they could have gotten an extra piece of a diplo card (at the same time you got an extra piece of,say, reinforcement ) which means they'll have a diplo card before you, and you'll have a reinf card before them